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3 years ago

Factorise fully the following:a) x² + 2xb) 2x² - 6xc) 15x - 10x³d) 9x² + 3x³

Mathematics

1 answer:

Lostsunrise [7]3 years ago

6 0

Answer:

a) $x(x+2)$

b) $2x(x-3)$

c) $5x(3-2x^2)$

d) $3x^2(3+x)$

Step-by-step explanation:

a) $x^2+2x$

When factoring a binomial (a polynomial with two terms), what we will be looking for are the terms that are shared between them.

In this problem, it can be seen that both of these terms have and x. This means that we can factor it out to get

$x(x+2)$

b) $2x^2-6x$

What are the common terms here?

It can be seen that each of these share a 2x, so our factored form would be

$2x(x-3)$

c) $15x-10x^3$

What about this one?

The common factor of this one is 5x, so our factored form would be

$5x(3-2x^2)$

d) $9x^2+3x^3$

The common factor of this one is $3x^2$ , so our factored form would be

$3x^2(3+x)$

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3 years ago

Please solve it I will give you 30 points

Aloiza [94]

Answer:

1. (2x^2+x-1)

Step-by-step explanation:

expanding (2x^2-1)^2. multiplying (x-2) (1-2x)

= 4x^2-4x+1. = x-2x^2-2+4x

= -2x^2+5x-2

(4x^2-4x+1-2x^2+5x-2)

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Answer:

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Step-by-step explanation:

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2 years ago

Suppose you are conducting a study to determine if women are better drivers than men. You send your survey to over 1000 students

julsineya [31]

Answer:

555.56

Step-by-step explanation:

Purpose of the study: To determine if women are better drivers than men.

Survey or Opinion population: 1,000

You are experimenting on 9 out of a thousand opinions.

5 of these opinions are that women are better drivers

4 of these opinions are that women are not better drivers

You want to know the <em>sample</em> (full sample size is 9) <em>proportion</em> for women as better drivers; using the large sample method. This method is also called the asymptotic method.

This involves approximating the desired statistic, with just a small fraction of the population; in this case, 9/1000.

This approximation will get more and more accurate as sample size increases and you know that a larger sample size gives a better representation and interpretation of the population preference!

So using ratio, the sample proportion for women as the better drivers is given by:

5/9 x 1000 = 555.56 opinions

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3 years ago

A publisher reports that 45% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is

nexus9112 [7]

Answer:

$z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933$

$p_v =2*P(z$

Step-by-step explanation:

Information given

n=370 represent the sample selected

$\hat p=0.4$ estimated proportion of readers owned a laptop

$p_o=0.45$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Creating the hypothesis

We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:

Null hypothesis: $p=0.45$

Alternative hypothesis: $p \neq 0.45$

The statistic is:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933$

Calculating the p value

We have a bilateral test so then the p value would be:

$p_v =2*P(z$

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3 years ago

Factorise fully the following:a) x² + 2xb) 2x² - 6xc) 15x - 10x³d) 9x² + 3x³​

Factorise fully the following:a) x² + 2xb) 2x² - 6xc) 15x - 10x³d) 9x² + 3x³